On Cyclic Descents for Tableaux
2018 ◽
Vol 2020
(24)
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pp. 10231-10276
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Keyword(s):
Abstract The notion of descent set, for permutations as well as for standard Young tableaux (SYT), is classical. Cellini introduced a natural notion of cyclic descent set for permutations, and Rhoades introduced such a notion for SYT—but only for rectangular shapes. In this work we define cyclic extensions of descent sets in a general context and prove existence and essential uniqueness for SYT of almost all shapes. The proof applies nonnegativity properties of Postnikov’s toric Schur polynomials, providing a new interpretation of certain Gromov–Witten invariants.
Keyword(s):
2016 ◽
Vol Vol. 18 no. 2, Permutation...
(Permutation Patterns)
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Keyword(s):
2002 ◽
Vol 357
(1428)
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pp. 1767-1779
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